Below I'll make some broad observations about the publication date progression of the F&GM stories, which is not the same as their ultimate in-world continuity (publication history taken from Wikipedia). Warning: There are SPOILERS liberally thrown around below.
Let's set aside the fact that, to a certain degree, Lieber went down the "re-order continuity and write some origin prequels" path (for a far more outrageous example: see Moorcock). There are really two major tonal changes that occur in the stories of the mid-1970's that gave me the feeling of the series precipitously falling out of its chair. These are the following:
On-Stage Appearance of the Gods. Prior to 1975, the gods never made physical appearance in the Lankhmar stories. While there are a legion of priests swarming the streets of the city and making a riotous noise to the gods in Lankhmar (detailed in stories such as "Lean Times in Lankhmar"), not a single one of them has magical powers, and to my reading they are clearly amusing showmen, charlatans, and frauds. Famously, Fafhrd is mistaken for the god Issek after being shaved, going on a drunken rampage, and miraculously shaking off a series of attackers' weapons (having been sabotaged in advance by the Mouser). If incidents such as this serve as the basis for the other of Lankhmar's various gods, then clearly the situation is not good for them -- and that's very much in the tradition of other works of pulp fiction being generally skeptical or dismissive of the nature of the church or religious men. The gods of early Fafhrd & the Gray Mouser are ambiguous in stature, quite probably just the product of con-men and/or delusions.
A prime example is in the first-published story, "Jewels in the Forest". A holy man follows F&GM into a dungeon-like structure, waving protective signs in the air. He declares: "For forty years I have lived on crusts and water, devoting my spirit to the Great God... My purpose in coming here is to destroy an evil thing... no harm can befall me. The hand of the Great God is poised above me, ready to ward off any danger that may threaten his faithful servant...!" -- and exactly one page later he is, ironically and unceremoniously, very dead. (As an aside, this 1939 story is otherwise fantastic and possibly the most thoroughly D&D-ish piece of writing that I've ever encountered.)
But: This changes dramatically with the 1975 short story "Under the Thumbs of the Gods". I was really rather shocked when the first page of this story introduces the "Land of the Gods" and a host of inhabitant deities bumping into each other and interacting, in particular the trio Kos, Issek, and Mog. The first two represent entities that Fafhrd had served or at least sworn idle oaths to in the past. The third is a spider-god with a rather ridiculous retcon of a back-story in that the Mouser had worshiped an idol of it to get in the graces of his first love -- ridiculous because in all the prior literature Mouser had been fervently and even exasperatingly skeptic and atheist. From this point forward, the gods routinely meddle in their affairs and curse them with a number of distracting ailments (up to and including permanent disfigurement). I was just really surprised by this total reversal in theme.
Settling on Rime Isle. The 1976 novelette "The Frost Monstreme" opens with the pair in their customary tavern:
Fafhrd shook his head morosely. 'We've never really lived. We've not owned land. We've not led men.'
'Fafhrd, you're gloomy-drunk!' the Mouser chortled. 'Would you be a farmer? Have you forgot a captain is the prisoner of his command? Here, drink yourself sober, or at least glad.'
The Northerner let his cup be refilled from two jars, but did not change his mood. Staring unhappily, he continued, 'We've neither homes nor wives.'
'Fafhrd, you need a wench!'
Now, when I first read this, I laughed heartily, thinking it to be a very clever anticipation of a classic Seinfeld scene:
Of course, after George & Jerry commit to getting married in a season cliffhanger, by the start of the next season, Jerry has abruptly broken it off with his carbon-copy fiance and returned to being much happier. (For George the problem lingers for a while longer.) So I was guffawing at how obviously identical this outcome would be for the pulp heroes in their analogous scene.
Except that Leiber wasn't really kidding with this exchange. Fafhrd & the Gray Mouser really do proceed within the story to assemble companies of men for them to gravely captain, to enter committed wife-like arrangements with two new women, and to land in permanent homes in the distant and ascetic community of Rime Isle. They will not ever again return to Lankhmar, or the Silver Eel tavern, or see their wizardly mentors Sheelba or Ningauble ever again in any of Leiber's stories.
In accordance with this shift of setting, the themes and tones of the narrative likewise shifts in a fairly dramatic fashion. We switch from Fafhrd & the Gray Mouser being wandering, thieving, active protagonists in the sword-and-sorcery picaresque style, to more responsible, reactionary, defend-the-land-from-invasions heroes, in the high fantasy style. In so doing, they become quite a bit less interesting, and simultaneously become mostly spectators, often saved by some outside phenomenon of which they are simply fortunate to be in the vicinity. To be charitable, we might say that this resembles the D&D tradition of high-level heroes switching to feudal rulership -- which either speaks poorly of its prospects for gaming, or emphasizes that the PCs must still remain the primary actors and not simply be blown around by setting events.